Geodesic
Interaction of Hecke–Shimura rings and zeta functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 5-14
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An automorphic structure on a Lie group consists of Hecke–Shimura ring of an arithmetical discrete subgroup and a linear representation of the ring on an invariant space of automorphic forms given by Hecke operators. The paper is devoted to interactions (transfer homomorphisms) of Hecke–Shimura rings of integral symplectic groups and integral orthogonal groups of integral positive definite quadratic forms. 
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A. Andrianov. Interaction of Hecke–Shimura rings and zeta functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a0/

[1] A. N. Andrianov, “The action of Hecke operators on nonhomogeneous theta series”, Mat. Sb. (N.S.), 131:3 (1986), 275–292 | MR | Zbl

[2] A. N. Andrianov, Quadratic Forms and Hecke Operators, Grundlehren math. Wiss., 286, Springer-Verlag, Berlin–Heidelberg, 1987 | DOI | MR | Zbl

[3] A. N. Andrianov, “Multiplicative properties of solutions of quadratic Diophantine problems”, Algebra Analiz, 2:1 (1990), 3–46 | MR | Zbl

[4] A. N. Andrianov, Queen's Lectures on Arithmetical Composition of Quadratic Forms, Queen's Papers in Pure and Applied Mathematics, 92, Queen's University, 1992 | MR | Zbl

[5] A. N. Andrianov, “Symmetries of harmonic theta-functions of integral quadratic forms”, Uspekhi Mat. Nauk, 50:4 (1995), 3–44 | MR | Zbl

[6] A. N. Andrianov, “Harmonic theta-functions and Hecke operators”, Algebra Analiz, 8:5 (1996), 1–31 | MR | Zbl

[7] A. N. Andrianov, “Around the Ikeda lift”, Funct. Analiz ego Prilozheniya, 35:2 (2001), 70–74 | DOI | MR | Zbl

[8] A. N. Andrianov, “Zeta functions of orthogonal groups of integral positive definite quadratic forms”, Uspekhi Mat. Nauk, 61:6(372) (2006), 3–44 | DOI | MR | Zbl

[9] A. N. Andrianov, “Interaction sums and action of Hecke operators on theta-series”, Acta Arithmetica, 140:3 (2009), 271–304 | DOI | MR | Zbl

[10] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, 1978 | MR | Zbl